We consider inflation in a universe with a positive cosmological constant and a nonminimally coupled scalar field , in which the field couples both quadratically and quartically to the Ricci scalar .
When considered in the Einstein frame and when the nonminimal couplings are negative , the field starts in slow roll and inflation ends with an asymptotic value of the principal slow roll parameter , \epsilon _ { E } = 4 / 3 .
Graceful exit can be achieved by suitably ( tightly ) coupling the scalar field to matter , such that at late time the total energy density reaches the scaling of matter , \epsilon _ { E } = \epsilon _ { m } .
Quite generically the model produces a red spectrum of scalar cosmological perturbations and a small amount of gravitational radiation .
With a suitable choice of the nonminimal couplings , the spectral slope can be as large as n _ { s } \simeq 0.955 , which is about one standard deviation away from the central value measured by the Planck satellite .
The model can be ruled out by future measurements if any of the following is observed : ( a ) the spectral index of scalar perturbations is n _ { s } > 0.960 ; ( b ) the amplitude of tensor perturbations is above about r \sim 10 ^ { -2 } ; ( c ) the running of the spectral index of scalar perturbations is positive .